A) there is no difference between saying "It either happens or it doesn't" and "There is a 40% chance it happens"

and, I assume, you also say that:

B) there is no difference between saying "It either happens or it doesn't" and "There is a 60% chance it happens"

So - unless you also have your own ideas of how logic works - you will also say that:

C) there is no difference between saying "There is a 40% chance it happens" and "There is a 60% chance it happens"

If there is no difference how could it be based on past experience or whatever?

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But maybe you didn't mean that and you recognize that saying that the probability is 60% means saying that it's more probable than when it's said that the probability is 40%.

It's clear that you don't like people using the word probability. However, the fact is that this use is completely in line with the mathematical definition of probability and with the meaning and etymology of "probable" (likely, reasonable, plausible, having more evidence for than against).